The four smallest cubic semisymmetric graphs are illustrated above. The smallest of these is Gray graph on 54 vertices, the next smallest
is the Iofinova-Ivanov graph on 110 vertices
(Iofinova and Ivanov 2002, Marušič et al. 2005), the third is
the Ljubljana graph (Conder et al. 2002),
and the fourth is the Tutte 12-cage.
Some cubic semisymmetric graphs are summarized in the following table.
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M.; Malnič, A.; Marušič, D.; Pisanski, T.; and Potočnik, P.
"The Edge-Transitive but Not Vertex-Transitive Cubic Graph on 112 Vertices."
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M. E. and Ivanov, A. A. "Bi-Primitive Cubic Graphs." In Investigations
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A. A. Ivanov, M. H. Klin, and A. J. Woldar). Dordrecht,
Netherlands: Kluwer, pp. 459-472, 1994.Ivanov, A. V. "On
Edge But Not Vertex Transitive Regular Graphs." In Combinatorial
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